SAT Subject Physics Practice Question 562: Answer and Explanation

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Question: 562

3. A 50 kg block slides down a plane that has been raised to an angle of 30° above the horizontal at a constant rate. After the block slides completely to the bottom of the plane, a rope is attached to the block. The rope pulls parallel to the surface of the plane as the block is pulled up the plane at a constant rate. Which statement about the tension in the rope is correct?

A. The tension in the rope is greater than the frictional force but less than the weight of the block.
B. The tension in the rope is greater than the frictional force plus the weight of the block.
C. The tension in the rope is equal to the weight of the block minus the frictional force.
D. The tension in the rope is equal to the weight of the block.
E. The tension in the rope is equal to the frictional force.

Correct Answer: D

Explanation:

The correct answer is (D). The block slides down the incline at a constant rate. This tells us that the frictional force (Ff) is equal to the force down the plane (F11). When the block is pulled up the plane at a constant rate, the force down the plane and the frictional force add together. The tension in the rope therefore equals the two of them. The inclined plane is at an angle of 30°, and the sine of 30° is .5, which when multiplied times the weight is equal to one half the weight of the block. The frictional force is also equal to half the weight of the block (Ff = F11), so the tension in the rope is equal to the sum of the two forces, which is equal to the weight of the block.

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